Machine Learning, Quantum Computing and Quantum Mechanics for Many Interacting Particles
Contents
What is this talk about?
Why? Basic motivation
More material
Basic activities, Overview
What has happened during the last two years
Machine Learning and Quantum Mechanics
Machine Learning and Physics
Lots of room for creativity
Types of Machine Learning
A simple perspective on the interface between ML and Physics
ML in a field like Nuclear Physics, Examples
More examples
Selected References
What are the basic ingredients?
Neural network types
Nuclear Physics Experiments Argon-46
Why Machine Learning?
Why Machine Learning for Experimental Analysis?
More arguments
The first theoretical system: electrons in a harmonic oscillator trap in two dimensions
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
Quantum Monte Carlo Motivation
The trial wave function
The correlation part of the wave function
Resulting ansatz
Energy derivatives
Derivatives of the local energy
How do we define our cost function?
Meet the variance and its derivatives
The variance defines the cost function
Why Boltzmann machines?
A standard BM setup
The structure of the RBM network
The network
Joint distribution
Defining different types of RBMs
Representing the wave function
Choose the cost/loss function
Running the codes
Energy as function of iterations, \( N=2 \) electrons
Energy as function of iterations, no Physics info \( N=2 \) electrons
Onebody densities \( N=6 \), \( \hbar\omega=1.0 \) a.u.
Onebody densities \( N=6 \), \( \hbar\omega=0.1 \) a.u.
Onebody densities \( N=30 \), \( \hbar\omega=1.0 \) a.u.
Onebody densities \( N=30 \), \( \hbar\omega=0.1 \) a.u.
Or using Deep Learning Neural Networks
Replacing the Jastrow factor with Neural Networks
Quantum Engineering
Candidate systems
Electrons (quantum dots) on superfluid helium
Quantum algorithms for solving many-body problems, simple model
More on the pairing model
Exact and Calculated Correlation Energies vs Pairing Strength for \( (p,n)=(4,2) \)
Exact and Calculated Correlation Energies vs Pairing Strength for \( (p,n)=(5,2) \)
Quantum Machine Learning
What kind of Machine Learning
More on Quantum Machine Learning
Possible Plans
Conclusions and where do we stand
Conclusions and where do we stand
What are the Machine Learning calculations here based on?
Additional Derivations
Unitary Coupled Cluster Ansatz
Technicalities
Mapping Pair Operators to Pauli Gates
Mapping the Ansatz
Trotter approximation
Mapping the Hamiltonian
More manipulations
Hamiltonian
Onebody densities \( N=6 \), \( \hbar\omega=1.0 \) a.u.
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